There has hitherto been known a control device for a continuously variable transmission connected to the output side of an engine. The control device controls the continuously variable transmission such that the output rotational speed of the engine is brought to a target rotational speed (see Patent Document 1, for example). In the case where deceleration which is determined by deceleration determination means which determines deceleration is large, the control device increases the target rotational speed stepwise, thereafter increases the target rotational speed at a predetermined gradient, and further decreases the target rotational speed at a predetermined lowering gradient which is based on the required deceleration. Consequently, it is possible for the engine to generate a braking force (engine brake force) by increasing the speed ratio, which is continuously variable, in the case where deceleration is large.